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*Unverified author*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 09 Dec 2008 09:57:50 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/09/t12288419554x4vcxibextupi1.htm/, Retrieved Sat, 25 May 2024 05:15:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31581, Retrieved Sat, 25 May 2024 05:15:55 +0000

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Estimated Impact

167

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F       [Standard Deviation-Mean Plot] [Toon Wouters] [2008-12-09 16:57:50] [14e94996a4178d938cb12bed20a4a373] [Current]

Feedback Forum

2008-12-15 18:42:33 [Steven Vercammen] [reply] 
Dit klopt. Het eerste wat we doen is kijken naar tabel 1: in deze tabel wordt een vergelijking weergegeven die het verband tussen het gemiddelde en de standaarddeviatie uitdrukt. Beta drukt hier de invloed van het gemiddelde op de standaarddeviatie uit, of nog: de helling van de regressielijn op de scatterplot op figuur 2. Alpha is een constante. De p-waarde is een getal dat uitdrukt of het gaat om een significant verband tussen het gemiddelde en de standaarddeviatie. Opdat dit het geval zou zijn moet deze waarde kleiner zijn dan 0.05. Dit is hier dus duidelijk het geval (0.001 < 0.05). We kunnen dus stellen dat beta significant verschilt van 0 er een wel degelijk een verband is tussen het gemiddelde en de standaardafwijking dat niet aan het toeval te wijten is. Bijgevolg bestaat er quasi-optimale Box-cox transformatie waarbij lambda als exponent wordt gebruikt van Yt. Wanneer de optimale lambda 0 is neemt men de ln van Yt. Deze optimale lambda lezen we af in de 2de tabel : -1.25

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31581&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31581&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31581&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	124.85	16.6721597008579	65.4
2	119.65	14.1673440123277	38.2
3	111.308333333333	12.1554670328984	39.7
4	113.133333333333	14.0631260803391	44
5	110.966666666667	11.7155943731059	38.6
6	109.608333333333	11.6752619852508	36.9
7	101.433333333333	10.4640799737468	35.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 124.85 & 16.6721597008579 & 65.4 \tabularnewline
2 & 119.65 & 14.1673440123277 & 38.2 \tabularnewline
3 & 111.308333333333 & 12.1554670328984 & 39.7 \tabularnewline
4 & 113.133333333333 & 14.0631260803391 & 44 \tabularnewline
5 & 110.966666666667 & 11.7155943731059 & 38.6 \tabularnewline
6 & 109.608333333333 & 11.6752619852508 & 36.9 \tabularnewline
7 & 101.433333333333 & 10.4640799737468 & 35.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31581&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]124.85[/C][C]16.6721597008579[/C][C]65.4[/C][/ROW]
[ROW][C]2[/C][C]119.65[/C][C]14.1673440123277[/C][C]38.2[/C][/ROW]
[ROW][C]3[/C][C]111.308333333333[/C][C]12.1554670328984[/C][C]39.7[/C][/ROW]
[ROW][C]4[/C][C]113.133333333333[/C][C]14.0631260803391[/C][C]44[/C][/ROW]
[ROW][C]5[/C][C]110.966666666667[/C][C]11.7155943731059[/C][C]38.6[/C][/ROW]
[ROW][C]6[/C][C]109.608333333333[/C][C]11.6752619852508[/C][C]36.9[/C][/ROW]
[ROW][C]7[/C][C]101.433333333333[/C][C]10.4640799737468[/C][C]35.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31581&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31581&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	124.85	16.6721597008579	65.4
2	119.65	14.1673440123277	38.2
3	111.308333333333	12.1554670328984	39.7
4	113.133333333333	14.0631260803391	44
5	110.966666666667	11.7155943731059	38.6
6	109.608333333333	11.6752619852508	36.9
7	101.433333333333	10.4640799737468	35.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-16.9531404615905
beta	0.264978843655933
S.D.	0.0412509675245952
T-STAT	6.42357887722134
p-value	0.00135762626224594

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -16.9531404615905 \tabularnewline
beta & 0.264978843655933 \tabularnewline
S.D. & 0.0412509675245952 \tabularnewline
T-STAT & 6.42357887722134 \tabularnewline
p-value & 0.00135762626224594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31581&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-16.9531404615905[/C][/ROW]
[ROW][C]beta[/C][C]0.264978843655933[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0412509675245952[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.42357887722134[/C][/ROW]
[ROW][C]p-value[/C][C]0.00135762626224594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31581&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31581&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-16.9531404615905
beta	0.264978843655933
S.D.	0.0412509675245952
T-STAT	6.42357887722134
p-value	0.00135762626224594

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.08141833743634
beta	2.25050062740054
S.D.	0.338491487564736
T-STAT	6.64861808960599
p-value	0.00116078108421521
Lambda	-1.25050062740054

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -8.08141833743634 \tabularnewline
beta & 2.25050062740054 \tabularnewline
S.D. & 0.338491487564736 \tabularnewline
T-STAT & 6.64861808960599 \tabularnewline
p-value & 0.00116078108421521 \tabularnewline
Lambda & -1.25050062740054 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31581&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-8.08141833743634[/C][/ROW]
[ROW][C]beta[/C][C]2.25050062740054[/C][/ROW]
[ROW][C]S.D.[/C][C]0.338491487564736[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.64861808960599[/C][/ROW]
[ROW][C]p-value[/C][C]0.00116078108421521[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.25050062740054[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31581&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31581&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-8.08141833743634
beta	2.25050062740054
S.D.	0.338491487564736
T-STAT	6.64861808960599
p-value	0.00116078108421521
Lambda	-1.25050062740054

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code